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SUMMARY:The F-KPP equation in the half-plane
DTSTART:20231205T085000Z
DTEND:20231205T095000Z
DTSTAMP:20240228T224300Z
UID:indico-event-11076@indico.math.cnrs.fr
DESCRIPTION:Speakers: Julien Berestycki\n\nIt has been shown by H. Beresty
cki and G. Cole (2022) that the F-KPP equation $\\partial_t u = \\frac{1
}{2}\\Delta u + u(1-u)$ in the half-plane with Dirichlet boundary conditio
ns admits travelling wave solutions for all speed $c\\ge c^*=\\sqrt{2}$.We
show that the minimal speed traveling wave $\\Phi$ is in fact unique (up
to shift) and give a probabilistic representation as the Laplace transform
of a certain martingale limit associated to the branching Brownian motion
with absorption. This representation allows us to study the asymptotic be
haviour of $\\Phi$ away from the boundary of the domain\, proving that\\be
gin{equation*} \\lim_{y \\to \\infty} \\Phi\\left(x + \\tfrac{1}{\\sqrt{2
}}\\log y\, y\\right) = w(x)\\end{equation*}where $w$ is the usual one-dim
ensional critical travelling wave.We are able to extend our result to the
case of the half-space $\\mathbb{H}^d =\\{x\\in R^d : x_1\\ge 0\\}$. Final
ly\, if time allows\, I will also mention some results regarding the conve
rgence towards the critical travelling wave.This is based on joint work wi
th Cole Graham\, Yujin Kim and Bastien Mallein.\n\nhttps://indico.math.cnr
s.fr/event/11076/
LOCATION:Salle Pellos (1R2-207) (IMT)
URL:https://indico.math.cnrs.fr/event/11076/
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